Donald Trump does not like to be interrupted. He banishes protesters from his rallies; a woman in a hijab garnered international prominence when she was removed from a campaign event earlier this month .

But there are exceptions to his rule. One morning this week, as a pack of Iowans gazed at the mogul-for-president without much wondering whether Sarah Palin would pop up next to him, Trump’s remarks on polling and winning and being “greedy for America” got cut off by the crowd – twice.

A woman near the stage was wearing his now trademark hat – bearing that slogan, “Make America Great Again” – which caught the attention of the candidate. Trump said he loved it, and she shouted: “I love you!”

Then there was the woman toward the back of the curtain-draped room in the corn-country suburb. This first-in-the-nation caucus state must be getting sick of him, Trump joked from behind his dais. “No!” the woman screamed out. “We love you!”

Trump grinned a toothy grin – this is the kind of interjection he likes, certainly more than the chants of “ a vote for Trump is a vote for hate ” that he was getting at a rally the previous evening.

For a macho candidate whose presidential pitch to female voters often amounts to “ I love women ”, Trumpophilia has set in with a shocking number of conservative women across this crucial bellwether, as his prospects for claiming the inaugural prize of the Republican nomination fight have climbed ever upward .

This despite Trump having openly insulted the looks of his party’s sole female contender, Carly Fiorina , the weight of Rosie O’Donnell, and the menstrual cycle of the Fox News anchor Megyn Kelly, and suggested Hillary Clinton got “ schlonged ” in her 2008 Democratic primary loss to Barack Obama – to begin a long list of misogynist moments on the trail.

If Trump is indeed gaffe-proof, it is not just the laws of politics that no longer conform in this year’s campaign but the landscape of gender: women of America, are you so entertained that you are not offended?

The Guardian conducted interviews this week with 18 women at four Trump events over 48 hours, including one hosted by John Wayne’s daughter and another where Palin was unveiled as the magnate’s new sidekick. The female supporters – including undecided voters – expressed views consistent with what the former vice-presidential candidate and the billionaire frontrunner agreed is nothing less than a “movement”: anti-establishment, unapologetic and, it turns out, gender-neutral. Not one said that she was turned off by his anti-women remarks.

These are qualities not fully reflected in the very polls Trump holds up as signifying his lead over the Texas senator Ted Cruz and a field of 10. Which is to say, the polls do not tell the whole Trump story. And such conversations offer a window into why Trump could be more popular than anyone ever thought possible.

“I believe it’s a non-gender issue,” said one woman of her choice. “I don’t see any issues about gender relations,” said another, adding: “I don’t even see that as being a problem in America.” As for anyone upset by Trump’s vulgar talk, or – dare a reporter ask it – thinking about a vote for Hillary Clinton instead: those women, the Trumpophiles say, are just trying to make America fail again.

“He’s sick and tired of things, and so am I,” exclaimed Judy Haines of Trump at the event in Norwalk. “You’re not allowed to say what you think.”

Nancy Young, a recently retired farmer from Arispe, Iowa, agreed. “This political correctness nonsense is causing us more harm than anything you can imagine,” she said on Tuesday in Winterset, from under the shadow of Wayne’s cowboy hat at his birthplace. “We have the freedom of speech in this country. Well, we can’t! You’re censored for everything you say.”

Trump’s call-it-as-you-see-it approach can seem relatively harmless to the masses, as when he uses it to poke fun at the “ low energy ” of Republican rival Jeb Bush. But in quiet conversation its effect takes on a severe afterglow.

After bemoaning the loss of free speech, Young went on to say she might have voted for Florida senator Marco Rubio but does not think he’s “eligible” for president, since his parents came from Cuba; she does not believe Barack Obama was born in the US ; and while she initially liked the retired neurosurgeon Ben Carson, she has changed her mind after seeing how his campaign has been managed.

There is a supposedly enlightened view among certain conservatives who claim they are not influenced by race issues. And Trump supporters, in declining to spell out meaningful differences in race or gender, approach their politics with a similarly intentional “blindness” that political scientists say is common across both parties – even Clinton’s.

He’ll offend people across the spectrum. You’re not going to change when he says it about a group to which you belong

Jennifer Lawless, academic

“Ever since we started research in 1998, party trumps gender every time,” said Adrienne Kimmell, executive director of the women’s equality group the Barbara Lee Foundation. “It’s true for both parties, but it’s particularly true for Republicans. So this construct that gender isn’t informing politics is very much what we have consistently found.”

Trump is “an equal opportunity offender”, said Jennifer Lawless, director of the Women and Politics Institute at American University. “He offends immigrants and women, he’ll offend people across the spectrum.” But typically supporters just chalk this up to brash straight talk, and, Lawless reasons, “you’re not going to change your mind when he says it about a group to which you belong”.

A poll of likely Republican voters in Iowa released this week showed Cruz tied with Trump among the party’s women in the state, at 23.5% support.

Anne Happel, 48, from Des Moines, said that while she does not identify as conservative, she does find Trump “refreshing” in his candor and decisiveness. “He doesn’t talk to us like we’re stupid,” she said. “He doesn’t talk down to anybody.”

Beyond the confines of the conservative base in Iowa, however, a new national poll found Trump was perceived negatively by 62% of women, compared with 32% for Cruz. Women comprise 52% of the US electorate – a number expected to skyrocket in November if Clinton is the Democratic nominee .

But don’t try telling the women who travel to see him that Trump is going away anytime soon.

Shelly Dee Martin said she liked Trump so much she changed her party affiliation from Democrat to Republican just to vote for him. “He’s a great businessman and a great golfer,” said Martin, who recently moved from California to Waukee, Iowa, for a job, leaving family behind. “I would think a lot of women would be against him because of all his marriages, but what you do in your private life is none of my business.”

“I am absolutely not a feminist,” said Olivia Otis in the college town of Ames, where she is in her first year at Iowa State University. “I respect who he is and I know a lot of women don’t respect him,” she said of Trump, “but … I don’t advocate that women are better than men – because I think, obviously, we’re equal. And I disagree that there’s a wage gap. I don’t think there is.”

The median US wage for men was $45,292 in 2014, according to the most recent available data ; for women, it was $37,388. Otis says she thinks any difference can be attributed to merit-based value.

Christi Gibson, a volunteer at Trump’s state headquarters in West Des Moines, also rejected gender as a political motivator, saying Trump’s support was born of a desire to repeal Obama’s healthcare policy, protect the right to bear arms, and ensure her pro-life values were upheld. She also felt she could trust him: “He’s never flip-flopped,” Gibson said.

Roxanne Johnston, who works at the John Wayne museum in Winterset , mostly admires Trump’s charisma, which inspired her to start watching the Republican debates. She said she also admires Trump’s plan to have Mexico pay for a wall at the US border. “Like the Berlin wall,” she exclaimed.

Her colleague Carol Merriam, who guides the museum’s tours, quickly interrupted: she remained at least one Republican woman in Iowa still holding out hope, somewhere beneath the shadow of John Wayne’s wax cowboy hat, for a female president.